High-level synthesis (HLS) is a rapidly evolving and popular approach to designing, synthesizing, and optimizing embedded systems. Many HLS methodologies utilize design space exploration (DSE) at the post-synthesis stage to find Pareto-optimal hardware implementations for individual components. However, the design space for the system-level Pareto-optimal configurations is orders of magnitude larger than component-level design space, making existing approaches insufficient for system-level DSE. This paper presents Pruned Genetic Design Space Exploration (PG-DSE)-an approach to post-synthesis DSE that involves a pruning method to effectively reduce the system-level design space and an elitist genetic algorithm to accurately find the system-level Pareto-optimal configurations. We evaluate PG-DSE using an autonomous driving application subsystem (ADAS) and three synthetic systems with extremely large design spaces. Experimental results show that PG-DSE can reduce the design space by several orders of magnitude compared to prior work while achieving higher quality results (an average improvement of 58.1x).